1 /*
2 *+
3 * Name:
4 * palAoppa
5
6 * Purpose:
7 * Precompute apparent to observed place parameters
8
9 * Language:
10 * Starlink ANSI C
11
12 * Type of Module:
13 * Library routine
14
15 * Invocation:
16 * void palAoppa ( double date, double dut, double elongm, double phim,
17 * double hm, double xp, double yp, double tdk, double pmb,
18 * double rh, double wl, double tlr, double aoprms[14] );
19
20 * Arguments:
21 * date = double (Given)
22 * UTC date/time (modified Julian Date, JD-2400000.5)
23 * dut = double (Given)
24 * delta UT: UT1-UTC (UTC seconds)
25 * elongm = double (Given)
26 * mean longitude of the observer (radians, east +ve)
27 * phim = double (Given)
28 * mean geodetic latitude of the observer (radians)
29 * hm = double (Given)
30 * observer's height above sea level (metres)
31 * xp = double (Given)
32 * polar motion x-coordinate (radians)
33 * yp = double (Given)
34 * polar motion y-coordinate (radians)
35 * tdk = double (Given)
36 * local ambient temperature (K; std=273.15)
37 * pmb = double (Given)
38 * local atmospheric pressure (mb; std=1013.25)
39 * rh = double (Given)
40 * local relative humidity (in the range 0.0-1.0)
41 * wl = double (Given)
42 * effective wavelength (micron, e.g. 0.55)
43 * tlr = double (Given)
44 * tropospheric lapse rate (K/metre, e.g. 0.0065)
45 * aoprms = double [14] (Returned)
46 * Star-independent apparent-to-observed parameters
47 *
48 * (0) geodetic latitude (radians)
49 * (1,2) sine and cosine of geodetic latitude
50 * (3) magnitude of diurnal aberration vector
51 * (4) height (hm)
52 * (5) ambient temperature (tdk)
53 * (6) pressure (pmb)
54 * (7) relative humidity (rh)
55 * (8) wavelength (wl)
56 * (9) lapse rate (tlr)
57 * (10,11) refraction constants A and B (radians)
58 * (12) longitude + eqn of equinoxes + sidereal DUT (radians)
59 * (13) local apparent sidereal time (radians)
60
61 * Description:
62 * Precompute apparent to observed place parameters required by palAopqk
63 * and palOapqk.
64
65 * Authors:
66 * TIMJ: Tim Jenness (JAC, Hawaii)
67 * {enter_new_authors_here}
68
69 * Notes:
70 * - It is advisable to take great care with units, as even
71 * unlikely values of the input parameters are accepted and
72 * processed in accordance with the models used.
73 *
74 * - The DATE argument is UTC expressed as an MJD. This is,
75 * strictly speaking, improper, because of leap seconds. However,
76 * as long as the delta UT and the UTC are consistent there
77 * are no difficulties, except during a leap second. In this
78 * case, the start of the 61st second of the final minute should
79 * begin a new MJD day and the old pre-leap delta UT should
80 * continue to be used. As the 61st second completes, the MJD
81 * should revert to the start of the day as, simultaneously,
82 * the delta UTC changes by one second to its post-leap new value.
83 *
84 * - The delta UT (UT1-UTC) is tabulated in IERS circulars and
85 * elsewhere. It increases by exactly one second at the end of
86 * each UTC leap second, introduced in order to keep delta UT
87 * within +/- 0.9 seconds.
88 *
89 * - IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.
90 * The longitude required by the present routine is east-positive,
91 * in accordance with geographical convention (and right-handed).
92 * In particular, note that the longitudes returned by the
93 * palObs routine are west-positive, following astronomical
94 * usage, and must be reversed in sign before use in the present
95 * routine.
96 *
97 * - The polar coordinates XP,YP can be obtained from IERS
98 * circulars and equivalent publications. The maximum amplitude
99 * is about 0.3 arcseconds. If XP,YP values are unavailable,
100 * use XP=YP=0.0. See page B60 of the 1988 Astronomical Almanac
101 * for a definition of the two angles.
102 *
103 * - The height above sea level of the observing station, HM,
104 * can be obtained from the Astronomical Almanac (Section J
105 * in the 1988 edition), or via the routine palObs. If P,
106 * the pressure in millibars, is available, an adequate
107 * estimate of HM can be obtained from the expression
108 *
109 * HM ~ -29.3*TSL*log(P/1013.25).
110 *
111 * where TSL is the approximate sea-level air temperature in K
112 * (see Astrophysical Quantities, C.W.Allen, 3rd edition,
113 * section 52). Similarly, if the pressure P is not known,
114 * it can be estimated from the height of the observing
115 * station, HM, as follows:
116 *
117 * P ~ 1013.25*exp(-HM/(29.3*TSL)).
118 *
119 * Note, however, that the refraction is nearly proportional to the
120 * pressure and that an accurate P value is important for precise
121 * work.
122 *
123 * - Repeated, computationally-expensive, calls to palAoppa for
124 * times that are very close together can be avoided by calling
125 * palAoppa just once and then using palAoppat for the subsequent
126 * times. Fresh calls to palAoppa will be needed only when
127 * changes in the precession have grown to unacceptable levels or
128 * when anything affecting the refraction has changed.
129
130 * History:
131 * 2012-08-24 (TIMJ):
132 * Initial version, ported directly from Fortran SLA.
133 * Adapted with permission from the Fortran SLALIB library.
134 * {enter_further_changes_here}
135
136 * Copyright:
137 * Copyright (C) 2012 Science and Technology Facilities Council.
138 * All Rights Reserved.
139
140 * Licence:
141 * This program is free software; you can redistribute it and/or
142 * modify it under the terms of the GNU General Public License as
143 * published by the Free Software Foundation; either version 3 of
144 * the License, or (at your option) any later version.
145 *
146 * This program is distributed in the hope that it will be
147 * useful, but WITHOUT ANY WARRANTY; without even the implied
148 * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
149 * PURPOSE. See the GNU General Public License for more details.
150 *
151 * You should have received a copy of the GNU General Public License
152 * along with this program; if not, write to the Free Software
153 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
154 * MA 02110-1301, USA.
155
156 * Bugs:
157 * {note_any_bugs_here}
158 *-
159 */
160
161 #include "math.h"
162
163 #include "pal.h"
164 #include "palmac.h"
165
166 /* These are local SLA implementations to aid in testing. Switch
167 * to native PAL implementations when tests are complete. */
168 static void pal__Geoc( double p, double h, double *r, double * z );
169 static void pal__Nutc ( double date, double * dpsi, double *deps, double * eps0 );
170 static double pal__Eqeqx( double date );
171
palAoppa(double date,double dut,double elongm,double phim,double hm,double xp,double yp,double tdk,double pmb,double rh,double wl,double tlr,double aoprms[14])172 void palAoppa ( double date, double dut, double elongm, double phim,
173 double hm, double xp, double yp, double tdk, double pmb,
174 double rh, double wl, double tlr, double aoprms[14] ) {
175
176 /* Constants */
177 const double C = 173.14463331; /* Speed of light (AU per day) */
178 const double SOLSID = 1.0027379093; /* Ratio between solar and sidereal time */
179
180 /* Local variables */
181 double cphim,xt,yt,zt,xc,yc,zc,elong,phi,uau,vau;
182
183 /* Observer's location corrected for polar motion */
184 cphim = cos(phim);
185 xt = cos(elongm)*cphim;
186 yt = sin(elongm)*cphim;
187 zt = sin(phim);
188 xc = xt-xp*zt;
189 yc = yt+yp*zt;
190 zc = xp*xt-yp*yt+zt;
191 if (xc == 0.0 && yc == 0.0) {
192 elong = 0.0;
193 } else {
194 elong = atan2(yc,xc);
195 }
196 phi = atan2(zc,sqrt(xc*xc+yc*yc));
197 aoprms[0] = phi;
198 aoprms[1] = sin(phi);
199 aoprms[2] = cos(phi);
200
201 /* magnitude of the diurnal aberration vector */
202 pal__Geoc(phi,hm,&uau,&vau);
203 aoprms[3] = PAL__D2PI*uau*SOLSID/C;
204
205 /* copy the refraction parameters and compute the a & b constants */
206 aoprms[4] = hm;
207 aoprms[5] = tdk;
208 aoprms[6] = pmb;
209 aoprms[7] = rh;
210 aoprms[8] = wl;
211 aoprms[9] = tlr;
212 palRefco(hm,tdk,pmb,rh,wl,phi,tlr,1e-10,
213 &aoprms[10],&aoprms[11]);
214
215 /* longitude + equation of the equinoxes + sidereal equivalent of DUT
216 * (ignoring change in equation of the equinoxes between UTC and TDB) */
217 aoprms[12] = elong+pal__Eqeqx(date)+dut*SOLSID*PAL__DS2R;
218
219 /* sidereal time */
220 palAoppat(date,aoprms);
221
222 }
223
224 /* Private reimplementation of slaEqeqx for testing the algorithm */
225
226 #include <math.h>
227
pal__Geoc(double p,double h,double * r,double * z)228 static void pal__Geoc( double p, double h, double *r, double * z ) {
229 /* earth equatorial radius (metres) */
230 const double A0=6378140.0;
231
232 /* reference spheroid flattening factor and useful function */
233 const double f = 1.0/298.257;
234 double b;
235
236 /* astronomical unit in metres */
237 const double AU = 1.49597870e11;
238
239 double sp,cp,c,s;
240
241 b = pow( 1.0-f, 2.0 );
242
243 /* geodetic to geocentric conversion */
244 sp = sin(p);
245 cp = cos(p);
246 c = 1.0/sqrt(cp*cp+b*sp*sp);
247 s = b*c;
248 *r = (A0*c+h)*cp/AU;
249 *z = (A0*s+h)*sp/AU;
250
251 }
252
pal__Eqeqx(double date)253 static double pal__Eqeqx( double date ) {
254
255 const double T2AS=1296000.0;
256
257 double pal_eqeqx;
258 double t, om, dpsi, deps, eps0;
259
260 /* interval between basic epoch j2000.0 and current epoch (jc) */
261 t=(date-51544.5)/36525.0;
262
263 /* longitude of the mean ascending node of the lunar orbit on the
264 * ecliptic, measured from the mean equinox of date */
265 om=PAL__DAS2R*(450160.280+(-5.0*T2AS-482890.539
266 +(7.455+0.008*t)*t)*t);
267
268 /* nutation */
269 pal__Nutc(date,&dpsi,&deps,&eps0);
270
271 /* equation of the equinoxes */
272 pal_eqeqx=dpsi*cos(eps0)+PAL__DAS2R*(0.00264*sin(om)+
273 0.000063*sin(om+om));
274
275 return pal_eqeqx;
276 }
277
278 #include "palmac.h"
279
pal__Nutc(double date,double * dpsi,double * deps,double * eps0)280 static void pal__Nutc ( double date, double * dpsi, double *deps, double * eps0 ) {
281
282 const double DJC = 36525.0;
283 const double DJM0 = 51544.5;
284 const double TURNAS = 1296000.0;
285
286 #define NTERMS 194
287
288 int j;
289 double t,el,elp,f,d,om,ve,ma,ju,sa,theta,c,s,dp,de;
290
291 int na[ 194 ][9] = {
292 { 0 , 0 , 0 , 0 , -1 , 0 , 0 , 0 , 0 },
293 { 0 , 0 , 2 , -2 , 2 , 0 , 0 , 0 , 0 },
294 { 0 , 0 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
295 { 0 , 0 , 0 , 0 , -2 , 0 , 0 , 0 , 0 },
296 { 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
297 { 0 , 1 , 2 , -2 , 2 , 0 , 0 , 0 , 0 },
298 { 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
299 { 0 , 0 , 2 , 0 , 1 , 0 , 0 , 0 , 0 },
300 { 1 , 0 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
301 { 0 , -1 , 2 , -2 , 2 , 0 , 0 , 0 , 0 },
302 { 0 , 0 , 2 , -2 , 1 , 0 , 0 , 0 , 0 },
303 { -1 , 0 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
304 { -1 , 0 , 0 , 2 , 0 , 0 , 0 , 0 , 0 },
305 { 1 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 },
306 { 1 , 0 , 0 , 0 , -1 , 0 , 0 , 0 , 0 },
307 { -1 , 0 , 2 , 2 , 2 , 0 , 0 , 0 , 0 },
308 { 1 , 0 , 2 , 0 , 1 , 0 , 0 , 0 , 0 },
309 { -2 , 0 , 2 , 0 , 1 , 0 , 0 , 0 , 0 },
310 { 0 , 0 , 0 , 2 , 0 , 0 , 0 , 0 , 0 },
311 { 0 , 0 , 2 , 2 , 2 , 0 , 0 , 0 , 0 },
312 { 2 , 0 , 0 , -2 , 0 , 0 , 0 , 0 , 0 },
313 { 2 , 0 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
314 { 1 , 0 , 2 , -2 , 2 , 0 , 0 , 0 , 0 },
315 { -1 , 0 , 2 , 0 , 1 , 0 , 0 , 0 , 0 },
316 { 2 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
317 { 0 , 0 , 2 , 0 , 0 , 0 , 0 , 0 , 0 },
318 { 0 , 1 , 0 , 0 , 1 , 0 , 0 , 0 , 0 },
319 { -1 , 0 , 0 , 2 , 1 , 0 , 0 , 0 , 0 },
320 { 0 , 2 , 2 , -2 , 2 , 0 , 0 , 0 , 0 },
321 { 0 , 0 , 2 , -2 , 0 , 0 , 0 , 0 , 0 },
322 { -1 , 0 , 0 , 2 , -1 , 0 , 0 , 0 , 0 },
323 { 0 , 1 , 0 , 0 , -1 , 0 , 0 , 0 , 0 },
324 { 0 , 2 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
325 { -1 , 0 , 2 , 2 , 1 , 0 , 0 , 0 , 0 },
326 { 1 , 0 , 2 , 2 , 2 , 0 , 0 , 0 , 0 },
327 { 0 , 1 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
328 { -2 , 0 , 2 , 0 , 0 , 0 , 0 , 0 , 0 },
329 { 0 , 0 , 2 , 2 , 1 , 0 , 0 , 0 , 0 },
330 { 0 , -1 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
331 { 0 , 0 , 0 , 2 , 1 , 0 , 0 , 0 , 0 },
332 { 1 , 0 , 2 , -2 , 1 , 0 , 0 , 0 , 0 },
333 { 2 , 0 , 0 , -2 , -1 , 0 , 0 , 0 , 0 },
334 { 2 , 0 , 2 , -2 , 2 , 0 , 0 , 0 , 0 },
335 { 2 , 0 , 2 , 0 , 1 , 0 , 0 , 0 , 0 },
336 { 0 , 0 , 0 , 2 , -1 , 0 , 0 , 0 , 0 },
337 { 0 , -1 , 2 , -2 , 1 , 0 , 0 , 0 , 0 },
338 { -1 , -1 , 0 , 2 , 0 , 0 , 0 , 0 , 0 },
339 { 2 , 0 , 0 , -2 , 1 , 0 , 0 , 0 , 0 },
340 { 1 , 0 , 0 , 2 , 0 , 0 , 0 , 0 , 0 },
341 { 0 , 1 , 2 , -2 , 1 , 0 , 0 , 0 , 0 },
342 { 1 , -1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
343 { -2 , 0 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
344 { 0 , -1 , 0 , 2 , 0 , 0 , 0 , 0 , 0 },
345 { 3 , 0 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
346 { 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 },
347 { 1 , -1 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
348 { 1 , 0 , 0 , -1 , 0 , 0 , 0 , 0 , 0 },
349 { -1 , -1 , 2 , 2 , 2 , 0 , 0 , 0 , 0 },
350 { -1 , 0 , 2 , 0 , 0 , 0 , 0 , 0 , 0 },
351 { 2 , 0 , 0 , 0 , -1 , 0 , 0 , 0 , 0 },
352 { 0 , -1 , 2 , 2 , 2 , 0 , 0 , 0 , 0 },
353 { 1 , 1 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
354 { 2 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 },
355 { 1 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
356 { 1 , 0 , -2 , 2 , -1 , 0 , 0 , 0 , 0 },
357 { 1 , 0 , 2 , 0 , 0 , 0 , 0 , 0 , 0 },
358 { -1 , 1 , 0 , 1 , 0 , 0 , 0 , 0 , 0 },
359 { 1 , 0 , 0 , 0 , 2 , 0 , 0 , 0 , 0 },
360 { -1 , 0 , 1 , 0 , 1 , 0 , 0 , 0 , 0 },
361 { 0 , 0 , 2 , 1 , 2 , 0 , 0 , 0 , 0 },
362 { -1 , 1 , 0 , 1 , 1 , 0 , 0 , 0 , 0 },
363 { -1 , 0 , 2 , 4 , 2 , 0 , 0 , 0 , 0 },
364 { 0 , -2 , 2 , -2 , 1 , 0 , 0 , 0 , 0 },
365 { 1 , 0 , 2 , 2 , 1 , 0 , 0 , 0 , 0 },
366 { 1 , 0 , 0 , 0 , -2 , 0 , 0 , 0 , 0 },
367 { -2 , 0 , 2 , 2 , 2 , 0 , 0 , 0 , 0 },
368 { 1 , 1 , 2 , -2 , 2 , 0 , 0 , 0 , 0 },
369 { -2 , 0 , 2 , 4 , 2 , 0 , 0 , 0 , 0 },
370 { -1 , 0 , 4 , 0 , 2 , 0 , 0 , 0 , 0 },
371 { 2 , 0 , 2 , -2 , 1 , 0 , 0 , 0 , 0 },
372 { 1 , 0 , 0 , -1 , -1 , 0 , 0 , 0 , 0 },
373 { 2 , 0 , 2 , 2 , 2 , 0 , 0 , 0 , 0 },
374 { 1 , 0 , 0 , 2 , 1 , 0 , 0 , 0 , 0 },
375 { 3 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
376 { 0 , 0 , 2 , -2 , -1 , 0 , 0 , 0 , 0 },
377 { 3 , 0 , 2 , -2 , 2 , 0 , 0 , 0 , 0 },
378 { 0 , 0 , 4 , -2 , 2 , 0 , 0 , 0 , 0 },
379 { -1 , 0 , 0 , 4 , 0 , 0 , 0 , 0 , 0 },
380 { 0 , 1 , 2 , 0 , 1 , 0 , 0 , 0 , 0 },
381 { 0 , 0 , 2 , -2 , 3 , 0 , 0 , 0 , 0 },
382 { -2 , 0 , 0 , 4 , 0 , 0 , 0 , 0 , 0 },
383 { -1 , -1 , 0 , 2 , 1 , 0 , 0 , 0 , 0 },
384 { -2 , 0 , 2 , 0 , -1 , 0 , 0 , 0 , 0 },
385 { 0 , 0 , 2 , 0 , -1 , 0 , 0 , 0 , 0 },
386 { 0 , -1 , 2 , 0 , 1 , 0 , 0 , 0 , 0 },
387 { 0 , 1 , 0 , 0 , 2 , 0 , 0 , 0 , 0 },
388 { 0 , 0 , 2 , -1 , 2 , 0 , 0 , 0 , 0 },
389 { 2 , 1 , 0 , -2 , 0 , 0 , 0 , 0 , 0 },
390 { 0 , 0 , 2 , 4 , 2 , 0 , 0 , 0 , 0 },
391 { -1 , -1 , 0 , 2 , -1 , 0 , 0 , 0 , 0 },
392 { -1 , 1 , 0 , 2 , 0 , 0 , 0 , 0 , 0 },
393 { 1 , -1 , 0 , 0 , 1 , 0 , 0 , 0 , 0 },
394 { 0 , -1 , 2 , -2 , 0 , 0 , 0 , 0 , 0 },
395 { 0 , 1 , 0 , 0 , -2 , 0 , 0 , 0 , 0 },
396 { 1 , -1 , 2 , 2 , 2 , 0 , 0 , 0 , 0 },
397 { 1 , 0 , 0 , 2 , -1 , 0 , 0 , 0 , 0 },
398 { -1 , 1 , 2 , 2 , 2 , 0 , 0 , 0 , 0 },
399 { 3 , 0 , 2 , 0 , 1 , 0 , 0 , 0 , 0 },
400 { 0 , 1 , 2 , 2 , 2 , 0 , 0 , 0 , 0 },
401 { 1 , 0 , 2 , -2 , 0 , 0 , 0 , 0 , 0 },
402 { -1 , 0 , -2 , 4 , -1 , 0 , 0 , 0 , 0 },
403 { -1 , -1 , 2 , 2 , 1 , 0 , 0 , 0 , 0 },
404 { 0 , -1 , 2 , 2 , 1 , 0 , 0 , 0 , 0 },
405 { 2 , -1 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
406 { 0 , 0 , 0 , 2 , 2 , 0 , 0 , 0 , 0 },
407 { 1 , -1 , 2 , 0 , 1 , 0 , 0 , 0 , 0 },
408 { -1 , 1 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
409 { 0 , 1 , 0 , 2 , 0 , 0 , 0 , 0 , 0 },
410 { 0 , 1 , 2 , -2 , 0 , 0 , 0 , 0 , 0 },
411 { 0 , 3 , 2 , -2 , 2 , 0 , 0 , 0 , 0 },
412 { 0 , 0 , 0 , 1 , 1 , 0 , 0 , 0 , 0 },
413 { -1 , 0 , 2 , 2 , 0 , 0 , 0 , 0 , 0 },
414 { 2 , 1 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
415 { 1 , 1 , 0 , 0 , 1 , 0 , 0 , 0 , 0 },
416 { 2 , 0 , 0 , 2 , 0 , 0 , 0 , 0 , 0 },
417 { 1 , 1 , 2 , 0 , 1 , 0 , 0 , 0 , 0 },
418 { -1 , 0 , 0 , 2 , 2 , 0 , 0 , 0 , 0 },
419 { 1 , 0 , -2 , 2 , 0 , 0 , 0 , 0 , 0 },
420 { 0 , -1 , 0 , 2 , -1 , 0 , 0 , 0 , 0 },
421 { -1 , 0 , 1 , 0 , 2 , 0 , 0 , 0 , 0 },
422 { 0 , 1 , 0 , 1 , 0 , 0 , 0 , 0 , 0 },
423 { 1 , 0 , -2 , 2 , -2 , 0 , 0 , 0 , 0 },
424 { 0 , 0 , 0 , 1 , -1 , 0 , 0 , 0 , 0 },
425 { 1 , -1 , 0 , 0 , -1 , 0 , 0 , 0 , 0 },
426 { 0 , 0 , 0 , 4 , 0 , 0 , 0 , 0 , 0 },
427 { 1 , -1 , 0 , 2 , 0 , 0 , 0 , 0 , 0 },
428 { 1 , 0 , 2 , 1 , 2 , 0 , 0 , 0 , 0 },
429 { 1 , 0 , 2 , -1 , 2 , 0 , 0 , 0 , 0 },
430 { -1 , 0 , 0 , 2 , -2 , 0 , 0 , 0 , 0 },
431 { 0 , 0 , 2 , 1 , 1 , 0 , 0 , 0 , 0 },
432 { -1 , 0 , 2 , 0 , -1 , 0 , 0 , 0 , 0 },
433 { -1 , 0 , 2 , 4 , 1 , 0 , 0 , 0 , 0 },
434 { 0 , 0 , 2 , 2 , 0 , 0 , 0 , 0 , 0 },
435 { 1 , 1 , 2 , -2 , 1 , 0 , 0 , 0 , 0 },
436 { 0 , 0 , 1 , 0 , 1 , 0 , 0 , 0 , 0 },
437 { -1 , 0 , 2 , -1 , 1 , 0 , 0 , 0 , 0 },
438 { -2 , 0 , 2 , 2 , 1 , 0 , 0 , 0 , 0 },
439 { 2 , -1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
440 { 4 , 0 , 2 , 0 , 2 , 0 , 0 , 0 , 0 },
441 { 2 , 1 , 2 , -2 , 2 , 0 , 0 , 0 , 0 },
442 { 0 , 1 , 2 , 1 , 2 , 0 , 0 , 0 , 0 },
443 { 1 , 0 , 4 , -2 , 2 , 0 , 0 , 0 , 0 },
444 { 1 , 1 , 0 , 0 , -1 , 0 , 0 , 0 , 0 },
445 { -2 , 0 , 2 , 4 , 1 , 0 , 0 , 0 , 0 },
446 { 2 , 0 , 2 , 0 , 0 , 0 , 0 , 0 , 0 },
447 { -1 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 },
448 { 1 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 },
449 { 0 , 1 , 0 , 2 , 1 , 0 , 0 , 0 , 0 },
450 { -1 , 0 , 4 , 0 , 1 , 0 , 0 , 0 , 0 },
451 { -1 , 0 , 0 , 4 , 1 , 0 , 0 , 0 , 0 },
452 { 2 , 0 , 2 , 2 , 1 , 0 , 0 , 0 , 0 },
453 { 2 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 },
454 { 0 , 0 , 5 , -5 , 5 , -3 , 0 , 0 , 0 },
455 { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 2 , 0 },
456 { 0 , 0 , 1 , -1 , 1 , 0 , 0 , -1 , 0 },
457 { 0 , 0 , -1 , 1 , -1 , 1 , 0 , 0 , 0 },
458 { 0 , 0 , -1 , 1 , 0 , 0 , 2 , 0 , 0 },
459 { 0 , 0 , 3 , -3 , 3 , 0 , 0 , -1 , 0 },
460 { 0 , 0 , -8 , 8 , -7 , 5 , 0 , 0 , 0 },
461 { 0 , 0 , -1 , 1 , -1 , 0 , 2 , 0 , 0 },
462 { 0 , 0 , -2 , 2 , -2 , 2 , 0 , 0 , 0 },
463 { 0 , 0 , -6 , 6 , -6 , 4 , 0 , 0 , 0 },
464 { 0 , 0 , -2 , 2 , -2 , 0 , 8 , -3 , 0 },
465 { 0 , 0 , 6 , -6 , 6 , 0 , -8 , 3 , 0 },
466 { 0 , 0 , 4 , -4 , 4 , -2 , 0 , 0 , 0 },
467 { 0 , 0 , -3 , 3 , -3 , 2 , 0 , 0 , 0 },
468 { 0 , 0 , 4 , -4 , 3 , 0 , -8 , 3 , 0 },
469 { 0 , 0 , -4 , 4 , -5 , 0 , 8 , -3 , 0 },
470 { 0 , 0 , 0 , 0 , 0 , 2 , 0 , 0 , 0 },
471 { 0 , 0 , -4 , 4 , -4 , 3 , 0 , 0 , 0 },
472 { 0 , 1 , -1 , 1 , -1 , 0 , 0 , 1 , 0 },
473 { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 },
474 { 0 , 0 , 1 , -1 , 1 , 1 , 0 , 0 , 0 },
475 { 0 , 0 , 2 , -2 , 2 , 0 , -2 , 0 , 0 },
476 { 0 , -1 , -7 , 7 , -7 , 5 , 0 , 0 , 0 },
477 { -2 , 0 , 2 , 0 , 2 , 0 , 0 , -2 , 0 },
478 { -2 , 0 , 2 , 0 , 1 , 0 , 0 , -3 , 0 },
479 { 0 , 0 , 2 , -2 , 2 , 0 , 0 , -2 , 0 },
480 { 0 , 0 , 1 , -1 , 1 , 0 , 0 , 1 , 0 },
481 { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 2 },
482 { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 },
483 { 2 , 0 , -2 , 0 , -2 , 0 , 0 , 3 , 0 },
484 { 0 , 0 , 1 , -1 , 1 , 0 , 0 , -2 , 0 },
485 { 0 , 0 , -7 , 7 , -7 , 5 , 0 , 0 , 0 }
486 };
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801 { 1.3999999999999999 , 0.0000000000000000 , 0.0000000000000000 , 0.0000000000000000 },
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808 { -2.3999999999999999 , 0.0000000000000000 , 0.0000000000000000 , 0.0000000000000000 },
809 { -18.399999999999999 , -0.10000000000000001 , 0.0000000000000000 , 0.0000000000000000 },
810 { 17.100000000000001 , 0.0000000000000000 , 0.0000000000000000 , 0.0000000000000000 },
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812 { 18.399999999999999 , 0.10000000000000001 , 0.0000000000000000 , 0.0000000000000000 },
813 { 0.0000000000000000 , 17.399999999999999 , 0.0000000000000000 , 0.0000000000000000 },
814 { -0.59999999999999998 , 0.0000000000000000 , 0.0000000000000000 , 0.0000000000000000 },
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818 { -2.0000000000000000 , 0.0000000000000000 , 0.0000000000000000 , 0.0000000000000000 },
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842 { -10.000000000000000 , 0.0000000000000000 , 0.0000000000000000 , 0.0000000000000000 },
843 { 9.5999999999999996 , 0.0000000000000000 , 0.0000000000000000 , 0.0000000000000000 },
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873 { 0.40000000000000002 , 12.000000000000000 , 0.29999999999999999 , -0.20000000000000001 },
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875 { 0.0000000000000000 , 0.0000000000000000 , 0.0000000000000000 , 0.0000000000000000 },
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878 };
879
880 /* interval between fundamental epoch j2000.0 and given epoch (jc). */
881 t = (date-DJM0)/DJC;
882
883 /* mean anomaly of the moon. */
884 el = 134.96340251*PAL__DD2R+
885 fmod(t*(1717915923.2178+
886 t*( 31.8792+
887 t*( 0.051635+
888 t*( - 0.00024470)))),TURNAS)*PAL__DAS2R;
889
890 /* mean anomaly of the sun. */
891 elp = 357.52910918*PAL__DD2R+
892 fmod(t*( 129596581.0481+
893 t*( - 0.5532+
894 t*( 0.000136+
895 t*( - 0.00001149)))),TURNAS)*PAL__DAS2R;
896
897 /* mean argument of the latitude of the moon. */
898 f = 93.27209062*PAL__DD2R+
899 fmod(t*(1739527262.8478+
900 t*( - 12.7512+
901 t*( - 0.001037+
902 t*( 0.00000417)))),TURNAS)*PAL__DAS2R;
903
904 /* mean elongation of the moon from the sun. */
905 d = 297.85019547*PAL__DD2R+
906 fmod(t*(1602961601.2090+
907 t*( - 6.3706+
908 t*( 0.006539+
909 t*( - 0.00003169)))),TURNAS)*PAL__DAS2R;
910
911 /* mean longitude of the ascending node of the moon. */
912 om = 125.04455501*PAL__DD2R+
913 fmod(t*( - 6962890.5431+
914 t*( 7.4722+
915 t*( 0.007702+
916 t*( - 0.00005939)))),TURNAS)*PAL__DAS2R;
917
918 /* mean longitude of venus. */
919 ve = 181.97980085*PAL__DD2R+fmod(210664136.433548*t,TURNAS)*PAL__DAS2R;
920
921 /* mean longitude of mars.*/
922 ma = 355.43299958*PAL__DD2R+fmod( 68905077.493988*t,TURNAS)*PAL__DAS2R;
923
924 /* mean longitude of jupiter. */
925 ju = 34.35151874*PAL__DD2R+fmod( 10925660.377991*t,TURNAS)*PAL__DAS2R;
926
927 /* mean longitude of saturn. */
928 sa = 50.07744430*PAL__DD2R+fmod( 4399609.855732*t,TURNAS)*PAL__DAS2R;
929
930 /* geodesic nutation (fukushima 1991) in microarcsec. */
931 dp = -153.1*sin(elp)-1.9*sin(2*elp);
932 de = 0.0;
933
934 /* shirai & fukushima (2001) nutation series. */
935 for (j=NTERMS-1; j >= 0; j--) {
936 theta = ((double)na[j][0])*el+
937 ((double)na[j][1])*elp+
938 ((double)na[j][2])*f+
939 ((double)na[j][3])*d+
940 ((double)na[j][4])*om+
941 ((double)na[j][5])*ve+
942 ((double)na[j][6])*ma+
943 ((double)na[j][7])*ju+
944 ((double)na[j][8])*sa;
945 c = cos(theta);
946 s = sin(theta);
947 dp += (psi[j][0] + psi[j][2]*t)*c + (psi[j][1] + psi[j][3]*t)*s;
948 de += (eps[j][0] + eps[j][2]*t)*c + (eps[j][1] + eps[j][3]*t)*s;
949 }
950
951 /* change of units, and addition of the precession correction.*/
952 *dpsi = (dp*1e-6-0.042888-0.29856*t)*PAL__DAS2R;
953 *deps = (de*1e-6-0.005171-0.02408*t)*PAL__DAS2R;
954
955 /* mean obliquity of date (simon et al. 1994). */
956 *eps0 = (84381.412+
957 (-46.80927+
958 (-0.000152+
959 (0.0019989+
960 (-0.00000051+
961 (-0.000000025)*t)*t)*t)*t)*t)*PAL__DAS2R;
962
963 }
964